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Question: If A = \(\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}\), then A<sup>2</sup> –4A...

If A = [122212221]\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}, then A2 –4A =

A

3 I

B

4 I

C

5I

D

None

Answer

5I

Explanation

Solution

Here A2 =[988898889]\begin{bmatrix} 9 & 8 & 8 \\ 8 & 9 & 8 \\ 8 & 8 & 9 \end{bmatrix}

A2 –4 A = [9−48−88−88−89−48−88−88−89−4]\begin{bmatrix} 9 - 4 & 8 - 8 & 8 - 8 \\ 8 - 8 & 9 - 4 & 8 - 8 \\ 8 - 8 & 8 - 8 & 9 - 4 \end{bmatrix}

= 5 [100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}= 5I